document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468327>Question 468327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Indicate the equation of the given line in standard form.<BR>\n" );
document.write( "The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).<BR>\n" );
document.write( "Place the symbols on the grid to complete the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321334 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find which line segment refers to the hypotenuse:<BR>\n" );
document.write( "Compute the following distances, PQ,PR,QR using the distance formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You should find the following:<BR>\n" );
document.write( "PQ = 5.65<BR>\n" );
document.write( "PR = 8.48<BR>\n" );
document.write( "QR = 10.19<BR>\n" );
document.write( "Verify it is a right triangle by showing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.65%5E2+%2B+8.48%5E2+=+10.19%5E2 ALIGN=MIDDLE  ALT=\"5.65%5E2+%2B+8.48%5E2+=+10.19%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore QR is the hypotenuse of this right triangle.<BR>\n" );
document.write( "The altitude or height of this triangle is represented by PQ.<BR>\n" );
document.write( "We need to determine the equation of the line passing through points P and Q.<BR>\n" );
document.write( "Determine slope of the line by using slope formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"m+=+%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P (-1,1)    Q(3,5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%285-1%29%2F%283-%28-1%29%29+=+4%2F4+=+1 ALIGN=MIDDLE  ALT=\"m+=+%285-1%29%2F%283-%28-1%29%29+=+4%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "slope of the line equals 1<BR>\n" );
document.write( "Point-slope form:<BR>\n" );
document.write( "(y -y1) = m(x - x1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+1+=+1%28x+-%28-1%29%29 ALIGN=MIDDLE  ALT=\"y+-+1+=+1%28x+-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+1+=+x+%2B+1 ALIGN=MIDDLE  ALT=\"y+-+1+=+x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x+%2B+2 ALIGN=MIDDLE  ALT=\"y+=+x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now it is in slope-intercept form<BR>\n" );
document.write( "They want it in standard form: Ax + By = C<BR>\n" );
document.write( "Just move the x to other side<BR>\n" );
document.write( "Subtract x on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+%2B+y+=+2 ALIGN=MIDDLE  ALT=\"-x+%2B+y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );